6. Consider an M/M/1 queuing system. The average inter-arrival time is 6 minutes

Question

6. Consider an M/M/1 queuing system. The average inter-arrival time is 6 minutes and the average service time is 5 minutes. What is the average number of customers in queue? Pick the closest value from the choices below. A. 0.83 C. 5 D. 0.42 7. Customers arrive at the local grocery store at a steady rate of 120 an hour. Thirty percent of these customers purchase 10 items or less and go to the express lines. Customers that don't meet the express line criterion go to the other regular checkout lines. It has been observed that on average there are 3 customers in the express checkout area. What is the average total time a customer needs to spend for express checkout? A. 3 minutes B. 5 minutes C. 6 minutes D. 10 minutes E. None of the above

Explanation / Answer

Answer to Question 6 :

Given are,

Arrival rate ( basis interarrival time of 6 minutes ) = a = 60/6 = 10

Service rate ( basis average service time of 5 minutes ) = s = 60/5 = 12

Average number of customers in the queue = a^2/ S x ( s -a ) = 10 x 10 / 12 x ( 12 – 10 ) = 100 /24 = 4.17

AVERAGE NUMBER OF CUSTOMERS IN THE QUEUE : B ) 4.17

Answer to Question 7 :

Arrival rate to the express line = a = 30 % of 120 per hour = 36 per hour = 0.6 per minute

Average total time a customer needs to spend at express checkout counter

= Average number of customers at checkout area / Arrival rate

= 3/ 0.6 minutes

= 5 minutes

ANSWER : B ) 5 MINUTES

AVERAGE NUMBER OF CUSTOMERS IN THE QUEUE : B ) 4.17

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